Whenever and Wherever: The Role of Card Acceptance
in the Transaction Demand for Money∗
Kim P. Huynh†
Philipp Schmidt-Dengler‡
Helmut Stix§
July 8, 2014
Abstract
The diffusion of payment cards, either credit or debit, is almost universal in developed economies.
Nevertheless, cash usage still remains widespread. We hypothesize that the lack of card acceptance at the point of sale is a key explanation why cash continues to play an important role. We
formulate a simple inventory model which predicts that the level of cash demand falls with an
increase in card acceptance. We use detailed payment diary data from Austrian and Canadian
consumers to test this model while accounting for the endogeneity of acceptance. Our results
confirm that card acceptance exerts a substantial impact on cash demand. The estimate of the
consumption elasticity (0.23 and 0.11 for Austria and Canada) is smaller than that predicted
by the classic Baumol Tobin inventory model (0.5). We conduct counterfactual experiments
and quantify the effect of increased acceptance on cash demand. Acceptance reduces both the
level of cash demand as well as its consumption elasticity.
Key Words: Inventory models of money, counterfactual distributions, Endogenous switching
regressions.
JEL Classification: E41, C35, C83.
∗
We thank Jason Allen, Karyne Charbonneau, Jan Schymik, and an OeNB working paper anonymous referee for
helpful comments. Angelika Welte and Anna Mitteregger provided outstanding research assistance. Schmidt-Dengler
gratefully acknowledges financial support from the German Science Foundation through Sonderforschungsbereich
Transregio 15. The views expressed in this paper are those of the authors. No responsibility for them should be
attributed to the Bank of Canada, the Oesterreichische Nationalbank, or the Eurosystem.
†
Bank of Canada, 234 Laurier Ave., Ottawa, ON K1A 0G9, Canada. Phone: +1 (613) 782 8698. E-mail:
[email protected].
‡
University of Mannheim, Department of Economics, L7 3-5, 68131 Mannheim, Germany, Phone: +49 621 181
1832. E-mail: [email protected]. Also affiliated with CEPR, CES-Ifo and ZEW.
§
Oesterreichische Nationalbank, Economic Studies Division, Otto-Wagner-Platz 3, A-1011 Vienna, Austria Phone:
+43 1 404 20 7205. E-mail: [email protected]
1
1 Introduction
Despite major improvements in payment technologies and their widespread diffusion over the past
decades, cash transactions still account for a large share of overall payment transactions, both
in terms of total number and value. Recent surveys show that more than half of the volume of
point-of-sales (POS) transactions are paid for with cash (83% in Austria and 53% in Canada).
The demand for cash has always been of considerable importance to policy makers, given that the
use of cash, its production and distribution is costly (see Segendorf and Jansson, 2012). From a
consumer’s perspective cash is expensive because of the cost of withdrawals (“shoe leather costs”
of going to the nearest ATM), the opportunity cost of holding a non-interest bearing asset (“welfare
cost of inflation”) and the risk of loss and theft.1
The workhorse model to study the demand for cash has been the Baumol-Tobin (BT) inventory
model (Baumol, 1952; Tobin, 1956) which predicts a consumption elasticity of cash demand of one
half. Recent studies have extended the BT model to study how the adoption of new payment and
withdrawal technologies affects the consumption and interest rate elasticities of cash demand and
hence the welfare cost of inflation, see Mulligan and Sala-i-Martin (2000), Attanasio, Guiso, and
Jappelli (2002), Lippi and Secchi (2009), Amromin and Chakravorti (2009), inter alia. Today, most
individuals (households) in developed economies have adopted one form or the other of modern
transaction technology: Our survey data indicate that 99% of Canadians and 86% of Austrians
own some type of payment card (debit or credit). Nevertheless, as mentioned above, cash usage is
universal while payment card usage is not. The main empirical question at this point thus becomes
what drives the intensive margin of cash use, when households have already adopted alternative
payment technologies.
This paper argues that the acceptance of payment cards at the POS plays a key role for the demand of cash. To study acceptance it is necessary to have transaction level data as acceptance varies
over different points of sale. We make use of data collected from large scale payment surveys by
the central banks of Austria (Oesterreichische Nationalbank) and Canada (Bank of Canada). The
need to account for acceptance in the analysis of cash demand is illustrated by Table 1 which
1
Humphrey, Willesson, Lindblom, and Bergendahl (2003) estimate that a country may save 1% of its GDP annually
as it shifts from a fully paper-based to a fully electronic-based payment system. Schmiedel, Kostova, and Ruttenberg
(2012) report estimates according to which half of the overall social cost of retail payments that arise for merchants,
banks and cash operators (amounting to almost 1% of GDP) can be attributed to cash usage.
2
provides key statistics from these payment surveys and contrasts them with predictions from prevailing theoretical models. Specifically, we focus on Alvarez and Lippi (2014) who establish in a
novel model a connection between withdrawals, average cash balances and the share of payments
made in cash. One prediction of this model is that cash is used whenever there is enough cash on
hand. The depletion of cash reserves before any cards are used is also central to the “Cash Holding”
model as described in Bouhdaoui and Bounie (2012). They show that the economy-wide aggregate
share of cash payments can be explained well by this type of model and that it performs better than
“Transaction Size” model by (Whitesell, 1989), where cards are only used for payment amounts
that are above a certain threshold value whereas all smaller transactions are paid for with cash.
Finally, experimental laboratory evidence from Camera, Casari, and Bortolotti (2014) illustrate the
importance of acceptance of electronic payments as usage generate benefits for consumers but may
carry the risk of being declined by merchants. They also find on the merchant side that increase
acceptance may result in more sales but comes at a cost which is an explanation why acceptance is
not necessarily universal.
Table 1 indicates that the data about cash holding practices are in line with newer versions of the
BT model. In Alvarez and Lippi (2009) and Alvarez and Lippi (2014) consumers face random free
withdrawal opportunities and withdraw at irregular intervals and at points in time when their cash
balances are still positive. Table 1 confirms that the average cash balance at withdrawal is around
e71 and CAD 63, respectively, significantly different from zero as the BT model would predict.
Still, Table 1 indicates that mechanisms beyond those in the “Cash Holding” and the “Transaction
Size” models must be driving the choice of using cash for payments. For a significant share of
transactions (12% in Austria and 35% in Canada) cards are used at some point for a transaction
rather than cash although respondents had enough cash on hand, i.e., where the cash holding type
models would have predicted the use of cash. Similarly, the largest cash transaction is often larger
than the smallest card transactions (observed for 69% of all respondents in Austria, and 29% in
Canada), even when conditioning on acceptance of payment cards (62% of all respondents in
Austria, and 23% in Canada) which is difficult to reconcile with the transaction size model. We
conclude from these results, that while the BT model and in particular its extensions have been
successful at capturing several key features of cash usage, it is necessary to take card acceptance
at the POS into account to understand households’ demand of cash.
3
To examine the role of acceptance for cash demand we study a simple extension of the BT
inventory model that accounts for heterogeneity in payment options available to consumers at the
POS.2 By explicitly accounting for cash and card payments we can consider total consumption
expenditures, and do not restrict attention to cash consumption as in Lippi and Secchi (2009),
Alvarez and Lippi (2009) and Bar-Ilan and Marion (2013). In our inventory model an increase in
acceptance causes individuals to reduce their cash holdings because they can use payment cards
more frequently. We proceed to estimate the cash demand equation derived from the model using
payment survey data.
We face the challenge that acceptance itself may be endogenous to cash holdings; respondents’
choice of vendor may depend on the cash they have on hand. Masters and Rodrı́guez-Reyes (2005)
use a search-theoretic framework to study the role of acceptance on cash usage. They explicitly
model merchants’ decision to accept cards, but assume that consumers are randomly matched with
merchants. While we do not model the merchant decision, our empirical strategy takes into account
that the choice of merchant may not be exogenous to the individual’s cash balance. This effect will
bias our estimates of the impact of acceptance on cash demand. We employ an empirical strategy
that corrects for the endogeneity of acceptance by using instruments when estimating cash demand.
We study the impact of acceptance on cash demand using data both at the person-level and at
the transaction-level. For both approaches we find that acceptance exerts a strong impact on the
demand for money. Our results also reveals that ignoring acceptance underestimates the consumption elasticity of money demand. The estimated consumption elasticities are significantly positive,
but less than one half as predicted by the BT model. Other key elements of cash demand stipulated
by the BT model, like shoe leather costs, risk of theft, etc., exert the predicted effect.
For the transaction-level regressions, we propose a switching regression model which separates
transactions into a non-acceptance and an acceptance regime. Our results confirm the existence of
two regimes which differ not only in the level of cash balances but also in the transaction elasticity
which is higher in the non-acceptance regime. Based on the point estimates of the regime switching
model we then predict how increased card acceptance at the POS will affect cash demand, a key
question for merchants and for central banks. Analysing the entire (counterfactual) distribution of
2
See McCallum and Goodfriend (1987) and applications in Mulligan and Sala-i-Martin (2000), Attanasio, Guiso,
and Jappelli (2002), and Amromin and Chakravorti (2009).
4
cash balances in the acceptance and in the non-acceptance regime shows that it is more compressed
in the acceptance regime. This result is consistent with the importance of lumpy purchases that
can only be paid for with cash (cf. Alvarez and Lippi, 2013). These payments account for most of
the heavy tail in the distribution of cash demand in a non-acceptance regime.
On a general note, using diary data from two separate countries allows us to examine the robustness of the results with respect to different institutional environments. Austria is a cash-intensive
country with mostly debit card users while Canada use less cash and favour credit cards. In this
respect, our findings show that many results obtained for Canada and Austria are qualitatively similar. This does not only hold for point estimates of key parameters but also for how acceptance
affects the level of cash balances.3
The remainder of this paper is organised as follows. Section 2 describes the payment diary
surveys from Canada and Austria and the data set we constructed from these surveys. Section 3
presents an extended BT inventory model accounting for acceptance of payment cards. Section
4 estimates cash demand equations at the individual level. Section 5 estimates an endogenous
switching regression model at the transaction level and performs counterfactuals to quantify the
role of acceptance on cash demand. Section 6 concludes.
2 Consumer Payment Diaries
We use data from payment diary surveys that have been conducted by the Oesterreichische Nationalbank (Austria) and the Bank of Canada. Survey respondents were asked to keep a diary and
record all payments over a pre-specified time period. Although the diary surveys were carried out
independently from each other, it turns out that they share key features with respect to the survey design and to the scope of collected information: (1) Both diaries record non-business related
personal expenditures with a strong focus on point-of-sale (POS) transactions. (2) The information collected for each transaction is very similar in the two surveys. All respondents were asked
to record (i) the transaction amount, (ii) the payment instrument used, (iii) the merchant’s sector
3
Our paper also contributes to the policy debate on the regulation of interchange fees and whether merchants should
be allowed to apply surcharges: Recent legislation in the US requires the Federal Reserve to regulate the interchange
fees for debit cards, Australia regulates credit card interchange, and the European Union recently started to regulate
cross-border interchange fees for credit cards. While this debate has so far been influenced by the question how this
policies would affect the adoption of card payment technologies it has given much less attention to how these policies
would influence the acceptance and consequently the actual use of payment cards.
5
and (iv) the day and the time-of-day. The respondents were also asked to assess whether (v) the
purchase could have been paid using payment instruments other than the one actually used, i.e.,
whether cards would have been accepted in case of a cash payment. (3) Both diaries collected
information on the timing as well as on the amount of cash withdrawals. Each diary furthermore
contained questions on consumers’ cash balances before the first recorded transaction. This allows
us to construct a cash stock measure for every transaction.
Table 2 summarizes the survey design of the data. The diaries differ with respect to the research
population (aged over 14 in Austria, and aged between 18 and 75 in Canada) and the recording
length (seven days for Austrian and three days for Canada). However, Canada has more respondents than Austria, 3283 compared to 1165. As a result, the number of transactions are not as
different due to the longer number of days (Austria) versus more respondents (Canada). Both
surveys sampled around the month of November but the Canadian study was conducted in 2009
versus 2011 for Austria.
Despite existing design differences, the survey outcomes concerning the structure of payments
were quite similar, on average. For example, the average number of daily transactions undertaken
per-person was 1.59 for Austria versus 1.66 for Canada. Survey respondents spent on average EUR
43 per-day in Austria and CAD 66 per-day in Canada. Applying a purchasing-power parity adjusted exchange rate, the per-person-per-day expenditures is similar between both countries. The
most prominent difference between the two countries is role of cash in total payments. Canadian
cash payments are usually small in transaction value as it only accounts for one fourth of the value
of transactions while in Austria it accounts for for almost two thirds of the value of transactions. As
a check on the overall validity of survey responses we compare the diary expenditures to national
income accounting aggregate consumption data. The resultant ratios are quite close to one (0.92
and 0.99 for Austria and Canada, respectively) indicating that the diaries give a quite accurate picture of household (non-housing) consumption expenditure—although these payment diaries were
not especially designed as consumption surveys. For a detailed description of payment diaries including Austria and Canada, seeBagnall, Bounie, Huynh, Kosse, Schmidt, Schuh, and Stix (2014).
The authors conduct a seven country comparison of cash and non-cash payments; present summary
statistics for key transaction characteristics that illustrate similarities and differences in Austria and
Canada; and discuss harmonization of measurement.
6
Each payment diary has two sections: one survey questionnaire that provides a detailed profile
of respondents and there cash management behaviour and two, a diary that tracks the transactions
that undertaken over a preset number of days. We conduct two sets of analysis for estimating
cash demand. The first set contains individual-level that consists of respondents’ average money
holdings and average payment behaviour over the diary sample period. This analysis is an attempt
to describe the average behaviour of respondents. The second set is a transaction level data: respondent’s cash holding at every transaction, combined with transaction characteristics and with
consumer characteristics.
All following results will be based on a comparable sample of respondents with an age of 18 or
older who own a payment card. This reduces the sample size mainly in Austria where the survey
also includes respondents from 14 to 18. In Austria only 86% are in possession of a payment
card (in Canada, 99% hold a payment card). We have made an effort to harmonize the sociodemographic variables and other control variables as closely as possible and are confident that
comparability is high enough to compare results for the two countries. Some variables will be used
that are only available in one of the two countries. In particular this is the case for variables we
use as instruments for acceptance. The Canadian survey recorded respondent’s assessment of the
number of cash registers at the point-of-sale. This information is not available in the Austrian data
where the POS terminal density is constructed at the municipality level from external data sources.
Also, our measures of shoe-leather costs and the risk of theft differ across countries. The variables
are described in Table A.1. While a full set of descriptive statistics are available in Table B.1-B.4.
3 Card Acceptance and Cash Demand
To derive an empirical specification for cash demand, we consider a parametric version of the
shopping time model by McCallum and Goodfriend (1987), who extended the classic BaumolTobin framework to account for shopping cost. Attanasio, Guiso, and Jappelli (2002) and Lippi
and Secchi (2009) have previously used versions of this model to account for the extensive margin
in the use of payment cards. We closely follow the notation in Attanasio, Guiso, and Jappelli
(2002) but offer an interpretation in terms of payment card acceptance.
7
3.1 The Transaction Demand for Cash
Consumers take time to make transactions (“shopping time”). Holding cash Mi reduces the time
τi it takes consumer i to finance her consumption ci . This time cost usually ascribed to the shadow
value of time and the fixed cost of withdrawing cash at the bank teller or the ATM. Let w denote
the opportunity cost of time. The cost of holding cash is the opportunity cost of holding a risk-free
asset paying interest rate R. An alternative to holding large amounts of cash is the use of payment
cards. Let si ∈ [0, 1] denote the share of consumer i’s consumption expenditure that can be paid
for with a payment card as given by merchant infrastructure. Finally, εi denotes consumer specific
unobservable factors affecting the time it takes to make transactions. The consumer thus minimises
the cost of holding money RMi plus the cost of transaction time τi w:
min
Mi
subject to
τi w + RMi
( )β
ci
τi =
eγsi +εi
Mi
Consumer i’s cash demand then becomes
(
) 1
β
wβeγsi +εi 1+β 1+β
Mi =
ci .
R
(1)
(2)
With β = 1 and γ = 0 this corresponds to the classic Baumol-Tobin model. These two parameters
measure the responsiveness of cash demand with respect to consumption expenditures and card
acceptance, respectively. Taking logs yields an estimable equation for cash demand
ln Mi = α̃ + β̃ ln ci + γ̃si + δ̃ ln R + ε˜i
(3)
where α̃ = (ln(wβ))/(1 + β), β̃ = β/(1 + β), γ̃ = γ/(1 + β), and ε˜i = (γ/(1 + β))εi . In earlier
empirical work, si has been interpreted as an indicator as to whether a consumer has adopted an
ATM card or not.4 Given almost universal adoption, we focus on explaining the role of acceptance
of these cards. We thus interpret si as a variable measuring whether a payment can be made with
cards.
Observe that the model treats si as exogenous to the consumer and we assume that si is given
by the consumer’s perception of merchants’ adoption of a card payment terminals. If si were
4
For example, Attanasio, Guiso, and Jappelli (2002) and Lippi and Secchi (2009) inter alia. Most debit cards can
be used to withdraw at ATMs.
8
indeed costless a costless option to the consumer, then it would be optimal for consumers to get
rid of cash as quickly as possible and always use cards whenever cards are accepted. The evidence
provided in Table 1 shows that this the case most of the time, but not always: consumers sometimes
pay with card although they had enough cash.5 While we address the potential endogeneity of si
when estimating (3), we will not be able to point to the source that causes it. Consequently, we will
not provide a structural interpretation to the estimated acceptance coefficient in equation (3). We
will interpret the coefficient as a reduced form capturing both the payment infrastructure offered
by merchants as well as consumers’ perception thereof. Our identification strategy outlined below
will try to account for both supply side effects (like the number of cash registers) as well as demand
effects (the payment behaviour of friends).
3.2 Estimating Cash Demand
Respondents in the surveys indicate whether cards were accepted at the point of sale for every
transaction they report. At the transaction level si is an indicator variable, at the person level
it denotes a continuous variable measuring the fraction of the individual’s payments in terms of
value that could have been made with cards. The goal of our empirical work is to quantify the
impact of acceptance si on cash demand Mi . Given that acceptance facilitates transactions with
payment cards, we expect si to reduce cash demand. The first challenge we face in estimating
the cash demand equation (3) is the potential measurement error in acceptance si because of false
reporting by survey respondents, resulting in a bias towards zero and underestimating the impact of
acceptance on cash-demand. The second challenge in estimating the cash demand equation is the
potential endogeneity of acceptance si itself: if a consumer has a lot of cash on hand (for instance
because of unexpected free withdrawal opportunity as in Alvarez and Lippi (2009)), she may be
more likely to visit a store that does not accept cards. Similarly, a consumer with no cash at hand
will avoid a cash-only store. This would cause a negative correlation between acceptance si and
the error term ε˜i resulting in an downward bias in our estimate of the coefficient of interest. We
will address these issues by employing appropriate econometric methods at the individual level
and at the transaction level, respectively, in the following sections.
5
We thank a referee for pointing this out, Alvarez and Lippi (2014) solve a related model where si is actually a
choice.
9
4 Individual-Level Cash Demand
To understand the cash demand Mi at the individual level i, we estimate the following relationship:
ln Mi = α̃ + β̃ ln ci + γ̃si + Xi λ + ε˜i ,
(4)
This corresponds to the cash demand equation (3) with the dependent variable measured in terms
of how much cash is held at the beginning of the diary. Consumption is the total amount of
expenditures over the diary collection period (ci ), and the share of acceptance is the fraction of
time that payment cards are accepted for each transaction undertaken. Finally, a vector of control
variables including socio-demographic information about individual i (gender, employment status,
age, household size), characteristics of her transactions (i.e., sectoral composition, transaction
value quartiles, time of day and day of the week variables) and information on shoe-leather costs
and the risk of theft denoted as Xi .
The results are summarized in Table 3.6 Column (1) contains the OLS estimate of consumption:
0.265 and 0.105 for Austria and Canada, respectively. The larger Austrian consumption elasticity
reflects that Austria is still a more cash intensive economy: Consumers hold more cash and pay
with cash more often. As a robustness check, we also consider cash consumption only in column
(2). As expected, the estimated coefficient magnitude is higher at 0.387 and 0.265 for Austria and
Canada, respectively. Adding acceptance as a regressor, columns (3) and (4), has no noticeable
effect on the consumption and cash consumption elasticity estimates themselves. The effect of
acceptance is however substantially smaller for cash consumption (and not significant for Austria).
This result further adds to the intuition that using only cash consumption increases the estimate
of the coefficient on consumption since it assumes that households pay for consumption only with
cash. Therefore, the households are more sensitive to changes in consumption. Moreover, given
that households pay only in cash, acceptance should not matter—which is what we find.7
6
For brevity, we suppress estimates for the control variables but provide the full set of NL-IV estimates in Appendix
Table A.1–A.2. The rest of the results are available from the authors upon request.
7
Our cash consumption elasticity estimates of 0.387 for Austria and 0.265 for Canada are broadly in line with those
of Lippi and Secchi (2009) for Italy (∼0.35).
10
4.1 Endogeneity of Acceptance
The simple shopping time model presented in Section 3 considered the share of transaction that
can be made with cash as entirely determined by the supply side. Respondents’ cash holdings may
however not only be affected by acceptance but rather their cash holdings may determine if they
transact at high or low acceptance stores. For example, if a respondent has low cash holdings then
she would care if the retailer accepts cards or not. In the cash consumption regression reported
in column (4), this decision is considered exogenous because all consumption is done in cash.
So, in column (5), we estimate a linear instrumental variable model (IV) and focus on the issue
of endogeneity of the acceptance variable. The empirical strategy relies on finding instrument(s)
that are correlated with acceptance but are not with individual cash holdings. The ideal candidates
for these instruments are physical characteristics of the point-of-sale as they are correlated with
acceptance but do not affect individual cash holdings.
The Canadian diary contains one such physical characteristic: the number of cash registers at
each transaction (as reported by respondents). These instruments were also used in Arango, Huynh,
and Sabetti (2014) who model the discrete choice of payment at the POS. For the individual-level
regressions, the instruments are person i’s share of stores with zero to two, three to six and more
than six cash registers. As these instruments are shares and do not have a symmetric distributions,
we use a third-order polynomial, as suggested by Lewbel (1997) and Escanciano, Jacho-Chávez,
and Lewbel (2012), to capture higher-order moments which may affect measurement error and
also increases the number of instruments available. For Austria, these variables are not available
and hence we use an alternative set of instruments: average acceptance in municipality in which
the respondent resides, payment behaviour of close friends and the share of shops with terminals
derived from administrative data (see Appendix A). The average acceptance in municipality is calculated from transactions reported by respondents residing in the same municipality as respondent
i, leaving out respondent i’s response. The rationale for using information regarding the payment
behaviour of close friends is that the usually shop in the same type of stores and have a comparable
consumption basket. We expect instruments measured at the municipality level rather than at the
person level not to perform as well as those used for Canada.
The IV estimates of column (5) depicts a significant effect of endogeneity acceptance as the
11
point estimate decreases from -0.519 to -1.332 for Austria and from -0.596 to -1.259 for Canada,
respectively. The consumption estimate does not materially change. The major impact of the
instrumenting for acceptance is that it increases the effect of acceptance on cash-holdings. We
implement two Wald F -tests of weak instruments, see Cragg and Donald (1993) and Kleibergen
and Paap (2006). There are no critical values for these weak instruments tests but we use the
tabulated test statistics calculated by Stock and Yogo (2005) and find that there is marginal evidence
of rejection of weak instruments in Austria and Canada. The linear IV estimate model works well
for Austria and Canada as the Hansen-Sargan tests of overidentification are not rejected. We next
address potential non-linearities in the share of acceptance in the the first stage regressions.
4.2 Functional Form of Acceptance
The share of acceptance for respondents with zero or one is 0.01 and 0.36 in Austria while for
Canada it is 0.09 and 0.33. Therefore, a non-trivial share lies between zero and one, hence the
assumption of linear IV may not be tenable. We therefore relax the functional form by employing
a nonlinear instrumental variables method and implement it in two-steps. In the first step we
model the share of acceptance as a fractional logit as suggested by Papke and Wooldridge (1996)
and compute the predicted shares (constrained between zero and one) and include them in a linear
second-stage regression. To address the generated regressor problem we bootstrap the regression
estimates 1000 times. For Canada, the effect of the non-linearities slightly reduces the effects of
both consumption and acceptance (0.111 to 0.109 for consumption and from -1.259 to -1.161 for
acceptance). For Austria, only the consumption elasticity is slightly reduced.
5 Transaction-Level Cash Demand
The previous analysis focused on average behaviour over the period of the diary. This aggregation
necessarily implies that for each individual household the temporal pattern of cash balances and
payment choices is averaged out over the period of the diary. However, the payment diaries contain observations at the transaction level: for each transaction we observe the transaction amount,
whether cards were accepted or not as well as many other transaction characteristics. We have also
computed the stock of cash held at each transaction. The richness of these data is likely to yield a
12
more precise representation of the cash holding-acceptance nexus.
Column (1) in Table 4 contains an OLS estimate of the elasticity of cash demand with respect
to transaction amount (consumption) and acceptance. Both coefficients are statistically significant.
The consumption elasticities are 0.176 and 0.099 for Austria and Canada, respectively. Acceptance
is also statistically and economically important with coefficients of -0.258 and -0.260 for Austria
and Canada, respectively. Column (2) utilizes instrumental variables to account for endogeneity
of acceptance. The instruments used are similar in the individual-level regression; for Austria they
are: average acceptance in municipality, payment behaviour of close friends and the share of shops
with terminals. The instruments for Canada are: a dummy indicating whether the store has three
to six cash registers and a dummy indicating whether the store has six or more cash registers. For
Canada, the instruments for acceptance variables at the transaction-level are binary so we cannot
use polynomials. It is not surprising that the IV results for Canada are not significant as the binary
nature of instruments causes a substantial increase in the standard errors for the regression. For
Austria the consumption elasticity is 0.229 and the effect of acceptance is -1.177.
5.1 Endogenous Switching Regression
The results from Canada illustrate the role of nonlinearities in the acceptance variable that is being
instrumented with binary variables. To address these nonlinearities we estimate a cash demand
equation using the endogenous switching regression suggested by Maddala (1983). The cash demand can be classified into two regimes, si = 1 if a card payment is accepted or zero otherwise:
si = 1 if γZi + ui > 0
si = 0 if γZi + ui ≤ 0
M 0 : ln M0i = α̃0 + β̃0 ln c0i + X0i λ0 + ϵ0i ,
(5)
M 1 : ln M1i = α̃1 + β̃1 ln c1i + X1i λ1 + ϵ1i .
Here, ln Mji denotes the natural logarithm of the cash stock of respondent i before each transaction, X0 and X1 are vectors of weakly exogenous variables, and β0 and β1 are the parameters of
interest.8 The error terms ui , ϵ0i and ϵ1i have a trivariate normal distribution, with mean vector zero
and well-defined covariance matrix. For an implementation of this method, see Lokshin and Sajaia
8
Again, these parameters are backed-out from the point-estimates of β̃0 and β̃1 according to equation (2).
13
(2006). The vector of control variables (Xi ) include: socio-demographic (gender, employment status, age, household size) and point-of-sale characteristics (sectoral composition, transaction value
quartiles, time of day and day of the week variables).9 For the regime equation variables (Zi ) are
the observables (Xi ) plus the exclusion restrictions. Again, the exclusion restrictions are the same
as in the linear IV in the individual level regression.
The results indicate that there are two regimes and that the selection is significant as both pvalue is less than 0.01. For Austria, Regime 1 (or the acceptance state) has a consumption elasticity
of 0.159 while Regime 0 (or the non-acceptance state) has a consumption elasticity of 0.233. Qualitatively similar results occur for Canada with 0.094 and 0.186 for Regime 1 and 0 respectively.
These results indicate that the nonlinearities plus the exclusion restrictions provide identification
for the model. The economic result of these elasticities state that when respondents are in nonacceptance areas, their cash demand is more inelastic than in acceptance areas, thus confirming
our earlier results now at the transaction level. Finally, the null hypothesis of no selection is also
rejected for both countries.
5.2 Counterfactual cash demand
The coefficient estimates of the switching show that there is a substantial effect of acceptance
on the elasticity of cash demand with respect to consumption. The well-identified model (5) of
cash demand can be used to construct counterfactual analyses that will allow us to quantify level
and distributional and distributional effects of acceptance. Specifically, the counterfactual scenario
we undertake is the following. We have two types of consumers, acceptance-type (A or “urban
dweller”) and non-acceptance-type (NA or “villager”). The terms “urban dweller” and “villager”
are used to indicate that acceptance is related to the two regimes (conditional densities). Conditional cash demand can be computed using
E(ln MCAj |si = CAj , Xi ) = Xi β0 + σCAj ρCAj
f (γZi )
,
F (γZi )
(6)
with card acceptance CAj ∈ {A, N A}.
Table 5 contains the means of three conditional distributions:
9
Control variables are defined in Table A.1. For brevity, we suppress estimates for the control variables. They are
are reported separately in A.3 for Austria and A.4 for Canada.
14
1. Baseline: the difference between “urban dwellers” and “villagers”.
2. A decrease in acceptance, i.e., an “urban dweller” that shops in a “village”.
3. An increase in acceptance, i.e., a “villager” that shops in the “city”.
These scenarios illustrate that the average difference between urban and villager cash demand
is about -19% and -23% for Austria and Canada, respectively. However, the effect of acceptance on
the types of respondents is quite asymmetric: increasing acceptance lowers cash demand by 32%
and 46% for both Austria and Canada, respectively. However, decreasing acceptance increases
cash demand by -26% and -19% for Austria and Canada, respectively. To ensure that the results
are not just an artefact of the shape of the distributions, Figure 1 plots the entire counterfactual
distributions for the scenarios described. The densities in the acceptance regime are red (light
grey), and the densities in the non-acceptance regime are green (dark grey). Again, a uniform
picture emerges for both Austria and Canada. In the acceptance regime the distribution is centered
at lower values and exhibits much lower variation than in the non-acceptance regime (top panels of
Figure 1). The non-acceptance regime is characterized by a center at higher values and a substantial
right tail, even for “urban dwellers”. This result is consistent with the presence of substantial lumpy
purchases that have to be paid for in cash. Again, moving the “villager” to the acceptance regime,
has a more pronounced effect on cash holding (middle panels of Figure 1) than moving a “urban
dwellers” to the non-acceptance regime (bottom panels of Figure 1).
These estimates have a strong prediction for the potential evolution of cash. As more POS
terminals are installed or cash demand will decrease. Besides this level effect of acceptance on
cash demand, we found a substantially smaller consumption elasticity in the acceptance regime
(see Table 4 ). This suggests, that card acceptance increases the velocity of cash: the deposit is
withdrawn and spent immediately with the card. As we move to the extreme case of universal
acceptance, the velocity of cash would become infinite and both the level of cash demand as well
as the consumption elasticity would approach zero.10
We not in this extreme world yet as the adoption of retail payment innovations are still speculative, see Fung, Huynh, and Sabetti (2012) or Chen, Felt, and Huynh (2014). Our results sug10
We thank a referee for alerting to this mechanism. Alvarez, Guiso, and Lippi (2012) illustrate this mechanism in
the context of durable goods purchases, where liquid assets required to purchase are durable are withdrawn and spent
immediately.
15
gest, that cash still has a precautionary component, i.e. serves as buffer for the possibility of
non-acceptance. The asymmetry of the effect of acceptance suggests that the precautionary nature is dominated by the supply-side effect of increased acceptance. There is also an element of
consumer-driven preferences especially for small value transactions as suggested by Wakamori
and Welte (2013).
5.3 Opportunity Cost of Cash
We next examine how the opportunity cost of holding cash affects cash demand. Earlier studies
mostly rely on cross-sectional or intertemporal variation in the nominal interest rate to measure
the opportunity cost. Given the short time horizon of the surveys (three and seven days), and the
absence of cross-sectional variation in deposit rates in Austria and Canada, an alternative measure
is needed to proxy for the opportunity costs of cash. Alvarez and Lippi (2009) use crime statistics
as a proxy for the probability of being robbed. Both the Austrian and the Canadian survey contain
subjective variables that are related to the risk of being robbed.
In the Austrian survey, a question elicited the amount of cash in the pocket which causes
respondents to feel uncomfortable. This variable, called risk of theft, is then mapped into a continuous probability (from 0 to 1). The risk of theft variable in Canada ask respondents about their
perception, on a scale of 1 (very unlikely) to 5 (very likely) about the probability of losing $20.
This variable does not match well with the Austrian risk of theft variable since it is not a continuous
variable as the question only pertains to the likelihood of losing a rather trivial amount. Another
possible reason is that Canadian respondents hold less cash than Austrians. Consequently, it is
not suitable as a proxy for shoe-leather cost. Instead, we follow the suggestion of Briglevics and
Schuh (2013) to focus on respondents who do not pay the complete balance of their credit card
statement at the due date and therefore incur interest charges or commonly known as revolvers. In
their study, they find that revolvers are a good proxy for interest elastic respondents as when they
face low cash balances and need to use cards they must weigh off the benefit of using a payment
card with the incurred cost of interest. Almost half of the sample of respondents (and transactions)
in Canada are revolvers.
The results in Table A.3 shows the effect of risk of theft for Austria. In the acceptance regime
the coefficient is -0.150 but insignificant while it is -0.349 in the non-acceptance regime and sig16
nificant. This highlights that when card payments are accepted the sensitivity to risk of theft of
cash is lower since there is less need to use or hold cash. The results in Table A.4 shows that in
the acceptance regime the coefficient on revolving is -0.180 while in the non-acceptance regime
it is -0.122. Both coefficients are significantly different from zero, but we cannot reject the null
hypothesis of them being equal. It shows, that when the opportunity cost of holding cash is high,
consumers become even more careful in managing there cash balances and keep them low. The
results highlight the use of these (imperfect) proxies for the opportunity cost of holding cash.
6 Conclusions
This paper analyzes how consumers manage their cash balances if they are uncertain whether
payment cards will be accepted. We adapt the stylized Baumol-Tobin cash inventory model to
account for card acceptance. We derive and estimate the resulting cash demand using payment
diary data from both Austria and Canada. Our estimation procedure accounts for endogeneity,
non-linearities and aggregation. We find that the extended Baumol-Tobin model yields robust
results across countries. Acceptance of payment cards has a strong impact on cash balances when
considering all consumption expenditures rather than only cash consumption as in Lippi and Secchi
(2009) and Alvarez and Lippi (2009).
Accounting for acceptance and its endogeneity implies smaller consumption elasticities than
predicted by the Baumol-Tobin model. We show that consumers behave differently depending on
whether they (choose to) shop in an environment where cards are accepted versus whether cards
are not accepted. Acceptance reduces both the level of cash demand as well as the transaction
elasticity of cash demand. Our counterfactuals show that increased acceptance would strongly
reduce cash demand. Cash demand in environments where cards are not accepted is partly driven
by precautionary motives or infrequent lumpy purchases that are paid in cash. We thus conclude
that pushing for increased acceptance will further reduce cash holdings, but not entirely eliminate
it, in part because of the mentioned precautionary motives but also some consumers’ preference
for using cash as discussed in Wakamori and Welte (2013).
17
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Table 1: Cash Management Behaviour
Austria Canada BT AL
Individual-level
M (mean)
133
84
+
+
M (median)
97
50
+
+
M (mean)
72
73
0
+
M (median)
39
30
0
+
(M /M ) (median)
0.29
0.60
0
+
Largest cash transaction larger
than smallest card transaction
0.69
0.29
.
0.00
. . . conditional on acceptance
0.62
0.23
.
0.00
Transaction-level
.
.
Enough cash on hand and:
. . . Card used
0.19
0.35
0.00 0.00
. . . standard deviation
0.39
0.48
.
.
Observations
5821
8725
Notes: M and M are cash on hand and minimum cash on hand before withdrawal, respectively. Figures
reported are in e and Canadian $. Largest cash transaction larger than smallest card transactions is the
proportion of respondents for which: (i) the buyer had enough cash and a card, and (ii) the seller accepted
both cash and card. Enough cash on hand and card used is the proportion of transactions where the amount
of cash in the wallet was sufficient to cover card purchases. These proportions were calculated for
transactions when the seller accepted both cash and card. BT and AL are theoretical predictions from
Baumol (1952), Tobin (1956) and Alvarez and Lippi (2009), respectively. A “.” was used to denote no
theoretical prediction.
20
Table 2: Payment Diary Design
Austria Canada
Collection Period Length (in Days)
7
3
Respondents
1,165
3,283
Year
2011
2009
Month
Oct-Nov
Nov
Sampling Frame
14+
18 - 75
Transactions
12,970
15,832
Transactions Per-Person-Day
1.59
1.66
Expenditures Per-Person-Day
49.63
50.32
Cash value share
0.65
0.23
Cash volume share
0.82
0.53
Diary-to-Aggregate Expenditure Ratio
0.92
0.99
Notes: This table is derived from the study of Bagnall, Bounie, Huynh, Kosse, Schmidt, Schuh, and Stix
(2014). The expenditures per-person-day (PPD) has been converted to purchasing power parity adjusted
US-Dollars to allow for comparison. The Diary-to-Aggregate Expenditure Ratio is computed by a simple
back-of-the envelope calculation. We calculate the total annual per person expenditure in local currency, by
multiplying the average PPD expenditure figure by 365. We compare this estimated annual consumption
figure with national accounts data from the OECD website taking into account that diaries do not cover
recurrent payments. We divide the calculated consumption expenditure by the total adult population. We
only consider adult individuals responding to the diary. By dividing by the total adult population we
implicitly assume that the responses to our diaries do not include consumption expenditure for minors.
21
Austria
Log consumption
Log cash consumption
Acceptance
adjusted R2
Log-Likelihood
Cragg & Donald F
Kleibergen & Paap F
Hansen-Sargan χ2
(p-value)
Observations
Canada
log consumption
Table 3: Individual-Level Cash Demand
(1)
(2)
(3)
(4)
OLS
OLS
OLS
OLS
0.265***
0.253***
[0.060]
[0.059]
0.387***
0.377***
[0.045]
[0.047]
-0.519***
-0.211
[0.170]
[0.174]
0.19
0.27
0.2
0.27
-949.67
-903.12
-945.08
-902.32
785
(1)
OLS
0.105***
[0.035]
log cash consumption
781
(2)
OLS
0.265***
[0.015]
Acceptance
adjusted R2
Log-likelihood
Cragg & Donald F
Kleibergen & Paap
Hansen Sargan χ2
(p-value)
Observations
0.07
-4498.86
0.18
-4313.87
2808
2808
785
(3)
OLS
0.108***
[0.034]
781
(4)
IV
0.252***
[0.015]
-0.596*** -0.220***
[0.068]
[0.069]
0.09
0.18
-4464.76
-4309.04
2808
2808
(5)
(6)
IV
NL-IV
0.240*** 0.234***
[0.058]
[0.066]
-1.332*
[0.738]
0.17
-956.73
10.17
9.25
2.7
0.44
785
(5)
IV
0.111***
[0.035]
-1.384**
[0.615]
0.19
-947.18
-1.259***
[0.417]
0.06
-4506.8
14.93
13.51
5.25
0.39
2808
-1.161***
[0.421]
0.07
-4494.58
785
(6)
NL-IV
0.109***
[0.036]
2808
Notes: OLS is ordinary least squares while IV is instrumental variables. The NLIV is nonlinear IV which
uses fractional logit of Papke and Wooldridge (1996) in the first stage to model the share of acceptance. For
brevity, we suppress the following control variables: socio-demographic variables (gender, employment
status, age, household size), point-of-sale characteristics (sectoral composition of expenditures, transaction
value quartiles, time of day and weekday) and country-specific measures of shoe-leather costs and risk of
theft. The instruments for Austria are: average acceptance in municipality, payment behaviour of close
friends, share of shops with terminals. The instruments for Canada are: share of stores with
3 ≤ cash registers ≤ 6, share of stores with cash registers > 6. Robust standard errors are in brackets in
columns (1-5) and in (6) they estimated via 1000 bootstrap replications; ***, ** and * denote 1, 5 and 10
percent significance levels respectively. A full set of NL-IV (6) estimates are available in Table A.1-A.2.
22
Table 4: Transaction-Level Cash Demand
(1)
(2)
Switching Regression
Austria
OLS
IV
Regime 1 Regime 0 Selection
Log transaction amount
0.176*** 0.229*** 0.159*** 0.233*** 0.472***
[0.016]
[0.027]
[0.020]
[0.029]
[0.078]
Acceptance
-0.258*** -1.177***
[0.038]
[0.394]
2
adjusted-R
0.16
0.05
Log-Likelihood
-8123.7
-8030.77
-9899.52
Cragg & Donald F
25.54
Kleibergen & Paap F
13.49
Hansen-Sargan χ2
3.81
(p-value)
0.43
H0 : No Selection (p-value)
<0.01
Observations
6157
5790
5790
(1)
(2)
Switching Regression
Canada
OLS
IV
Regime 1 Regime 0 Selection
Log consumption
0.099*** 0.104*** 0.094*** 0.186*** 0.483***
[0.010]
[0.025]
[0.015]
[0.041]
[0.044]
Acceptance
-0.260***
-0.274
[0.027]
[0.231]
adjusted R2
0.06
0.06
Log-likelihood
-15061.81 -15062.09
-20067.95
Cragg & Donald F
45.69
Kleibergen & Paap F
48.84
2
Hansen-Sargan χ
19.59
(p-value)
0
Ho: No selection (p-value)
<0.01
Observations
10020
10020
10020
Notes: OLS and IV are the ordinary least squares and instrumental variable estimates. For brevity, we
suppress the following control variables: socio-demographic variables (gender, employment status, age,
household size), point-of-sale characteristics (sectoral composition of expenditures, transaction value
quartiles, time of day and weekday) and country-specific measures of shoe-leather costs and risk of theft.
The switching regression displays the two regimes and the selection equation. The exclusion restrictions
for Austria are: average acceptance in municipality, payment behaviour of close friends, share of shops
with terminals. The exclusion restrictions for Canada are: if the store has 3 ≤ cash registers ≤ 6, if the
store had cash registers > 6. Standard errors clustered by person are in brackets and ***, ** and * denote
1, 5 and 10 percent significance levels respectively. A full set of switching regression estimates are
available in Table A.3-A.4.
23
Table 5: Counterfactual Cash Holdings
Austria Canada
in e
in $
M for
. . . villager shopping in village E[M − N A|N A]
. . . urban dweller shopping in city E[M − A|A]
% change
M for villager given that (s)he
. . . shops in village E[M − N A|N A]
. . . shops in city E[M − N A|A]
% change
M for urban dweller given that (s)he
. . . shops in city E[M − A|A]
. . . shops in village E[M − A|N A]
% change
105.8
85.1
-19%
65.5
53.1
-23%
105.8
69.9
-32%
65.5
35.6
-46%
85.1
106.8
+26%
53.1
63.5
+19%
Notes: Villager is an illustrative term for the low acceptance (NA) regime while urban dweller
refers to the high acceptance (A) regime. We use the following conditional expectation to
compute the counterfactual cash holdings:
E(ln MCAj |si = CAj , Xi ) = Xi β0 + σCAj ρCAj
f (γZi )
F (γZi )
with card acceptance CAj ∈ A, N A. The distributional aspect of this exercise is available in
Figure 1.
24
Figure 1: Counterfactual scenarios
2
1
0
0
1
2
3
Canada
3
Austria
0
1
2
Cash on Hand
3
0
1
2
Cash on Hand
3
E[M−NA | NA]
E[M−A | A]
1
3
4
2
1
0
0
1
2
3
E[M−A | A]
3
E[M−NA | NA]
4
1
2
Cash on Hand
3
4
E[M−NA | A]
1
3
2
Cash on Hand
E[M−NA | NA]
E[M−NA | A]
1
3
4
2
1
0
0
1
2
3
E[M−NA | NA]
0
3
0
0
2
Cash on Hand
E[M−A | NA]
4
0
E[M−A | A]
2
Cash on Hand
E[M−A | NA]
4
E[M−A | A]
Notes: These graphs correspond to the counterfactual scenarios computed from the switching
regression model. The average effects are reported and correspond to the row elements in Table 5.
The top row displays the expected cash demand (M ) distributions for those in low acceptance
(N A) and high acceptance (A). The second row displays the cash distribution of the
non-acceptance regime conditional on N A and A. The last row displays the cash distribution of
the acceptance regime conditional on N A and A.
25
Table A.1: Variable Definitions
Austria
Canada
Individual-level control variables
Consumption
value of expenditures recorded in the value of expenditures recorded in the
diary
diary
Cash consumption value of cash expenditures recorded in value of cash expenditures recorded in
the diary
the diary
Acceptance
share of transactions at which card pay- share of transactions at which card payments were possible (value weighted)
ments were possible (value weighted)
Sociogender, employment status (unemp., gender, employment status (unemp.,
demographic
employed, retired), household income employed, retired), household income
variables
tercils, education (3 categories), house- tercils, education (3 categories), household size (3 categories), household hold size (3 categories), household
head
head
dummy variable for existence of cash
income
Risk of theft / shoe- perceived risk of theft (calculated Revolving credit is an indicator
leather costs
from survey responses on amount in whether the respondent did not pay
the pocket which causes respondents the full balance of their credit card
to feel uncomfortable (exponentially and incurred interest charges on their
transformed 0 (no risk) to 1). Respon- account.
dents who indicated that they never feel
uncomfortable carrying large amounts
of money in their pocket were assigned
a value of 0), ATM density (# of ATMs
within 2 km around respondents’ residence)
Transaction char- expenditure share for each day of the week, for each payment type (6
acteristics
categories) and for transaction value quartiles
expenditure share for time of the day expenditure share for time of the day
(AM, PM, late PM)
(AM, PM)
Transaction-level control variables
for transaction level regressions we employ a set of dummy variables
for the day-of-the week, the payment type/location, the time of the day.
Instruments
1) share of acceptance reported by 1) share of transactions with 0 to 2 regother survey respondents within a mu- isters, 3 to 6 registers and more than 6
nicipality (source: survey), 2) payment registers (for each transaction responbehaviour of close friends (source: sur- dents report number of cash registers at
vey question), 3) share of shops in payment locations)
muncipality with 0 terminals, 1 terminal, 2 or more terminals (source:
terminal location for 2005 from payment service providers, information on
shops from 2011 data from Austrian
statistical office)
26
Table A.2: Individual-Level Cash Demand Austria: Nonlinear IV Model
Log consumption
Acceptance
ATM density
Risk of theft
Female
Unempl.
Other empl.
Student
Income Q2
Income Q3
Age 36-60
Age 60+
Edu med
Edu high
HH size 2-4
HH size 4+
HH head
(6)
NL-IV
0.234***
[0.066]
-1.384**
[0.615]
-0.100**
[0.043]
-0.247***
[0.090]
-0.253***
[0.071]
-0.078
[0.148]
0.044
[0.146]
-0.062
[0.164]
0.052
[0.080]
0.166*
[0.097]
0.137*
[0.081]
0.276
[0.173]
-0.276***
[0.098]
-0.205***
[0.075]
0.067
[0.080]
0.073
[0.169]
0.196***
[0.073]
Note: The table reports the second stage results of the NL-IV model for Austria, i.e. column (6) of Table 3.
Standard errors are in brackets and are estimated via 1000 bootstrap replications; ***, ** and * denote 1, 5
and 10 percent significance levels respectively. The instruments for Austria are: average acceptance in
municipality, payment behaviour of close friends, share of shops with terminals. The table continues on the
next page.
27
Table A.1: Individual-Level Cash Demand Austria: Nonlinear IV Model (Continued)
Share gas stations
Share (semi)durables
Share services
Share restaurant/bar
Share other exp.
Share TV Q2
Share TV Q3
Share TV Q4
Share AM
Share late PM
Share sunday
Share monday
Share tuesday
Share wednesday
Share thursday
Share friday
Constant
adjusted R2
Log-Likelihood
Observation
(6)
NL-IV
0.599**
[0.267]
-0.012
[0.186]
-0.500
[0.328]
-0.112
[0.283]
-0.475
[0.297]
0.402
[0.369]
0.391
[0.312]
0.419
[0.337]
0.312**
[0.128]
-0.183
[0.191]
-0.017
[0.348]
0.337
[0.262]
-0.102
[0.251]
0.313
[0.264]
0.119
[0.279]
0.400*
[0.241]
3.826***
[0.651]
0.19
-947.18
785
Note: The table reports the second stage results of the NL-IV model for Austria, i.e. column (6) of Table 3.
Standard errors are in brackets and are estimated via 1000 bootstrap replications; ***, ** and * denote 1, 5
and 10 percent significance levels respectively. The instruments for Austria are: average acceptance in
municipality, payment behaviour of close friends, share of shops with terminals.
28
Table A.2: Individual-Level Cash Demand Canada: Nonlinear IV Model
Log consumption
Revolving credit
Acceptance
Age 36-60
Age 60+
Educ. med
Educ. high
Female
Part-time
Unemployed
Retired
Income Q2
Income Q3
HH size 2-4
HH size 4+
(6)
NL-IV
0.117***
[0.036]
-0.263***
[0.048]
-1.180***
[0.420]
0.265***
[0.061]
0.453***
[0.095]
-0.094
[0.062]
-0.045
[0.069]
0.204***
[0.049]
-0.05
[0.071]
-0.132
[0.094]
0.002
[0.076]
-0.06
[0.057]
0.133*
[0.073]
-0.043
[0.057]
-0.044
[0.111]
Note: The table reports the second stage results of the NL-IV model for Canada, i.e. column (6) of Table 3.
The instruments for Canada are: share of stores with 3 ≤ cash registers ≤ 6, share of stores with
cash registers > 6. Standard errors are in brackets and are estimated via 1000 bootstrap replications; ***,
** and * denote 1, 5 and 10 percent significance levels respectively. The table continues on the next page.
29
Table A.2: Individual-Level Cash Demand Canada: Nonlinear IV Model (Continued)
Gasoline value share
Personal attire value share
Healthcare value share
Hobby/Sporting value share
Services value share
TVQ2 value share
TVQ3 value share
TVQ4 value share
AM value share
Weekend value share
Constant
adjusted R2
Log-likelihood
Observations
(6)
NL-IV
0.177
[0.118]
-0.049
[0.097]
-0.132
[0.178]
0.112
[0.110]
-0.235*
[0.133]
0.545***
[0.198]
0.556***
[0.194]
0.672***
[0.232]
0.05
[0.067]
0.088
[0.062]
3.371***
[0.277]
0.08
-4479.27
2808
Note: The table reports the second stage results of the nonlinear IV model for Canada, i.e. column (6) of
Table 3. The instruments for Canada are: share of stores with 3 ≤ cash registers ≤ 6, share of stores with
cash registers > 6. Standard errors are in brackets and are estimated via 1000 bootstrap replications; ***,
** and * denote 1, 5 and 10 percent significance levels respectively.
30
Table A.3: Transaction-Level Cash Demand Austria: Switching Regression Model
Log transaction amount
Regime 1
0.159***
[0.020]
Regime 0
0.233***
[0.029]
-0.119***
[0.039]
-0.150
[0.092]
-0.218***
[0.074]
-0.003
[0.175]
0.180
[0.126]
-0.152
[0.189]
0.120
[0.084]
0.354***
[0.101]
0.145
[0.096]
0.282*
[0.160]
-0.139
[0.100]
-0.160**
[0.080]
0.023
[0.077]
0.097
[0.148]
0.114
[0.112]
0.057
[0.039]
-0.061
[0.058]
-0.076
[0.085]
-0.139***
[0.053]
-0.079*
[0.045]
-0.349***
[0.122]
-0.134
[0.084]
-0.061
[0.198]
-0.158
[0.192]
-0.294
[0.246]
-0.032
[0.114]
0.202*
[0.105]
0.111
[0.112]
0.623***
[0.224]
0.039
[0.121]
-0.159*
[0.095]
0.013
[0.108]
0.073
[0.178]
0.120
[0.122]
0.088
[0.069]
0.067
[0.071]
0.144
[0.100]
0.141
[0.086]
Log transaction amount2
ATM density
Risk of theft
Female
Unempl.
Other empl.
Student
Income Q2
Income Q3
Age 36-60
Age 60+
Edu med
Edu high
HH size 2-4
HH size 4+
Cash income
AM
Late PM
Sunday
Tuesday
Selection
0.472***
[0.078]
-0.048***
[0.015]
0.016
[0.039]
0.146*
[0.087]
-0.038
[0.069]
-0.089
[0.163]
0.179
[0.110]
0.020
[0.161]
-0.098
[0.087]
-0.160*
[0.087]
-0.010
[0.089]
-0.505***
[0.145]
-0.160*
[0.084]
-0.058
[0.076]
-0.244***
[0.069]
-0.606***
[0.155]
-0.036
[0.111]
-0.083
[0.059]
-0.274***
[0.074]
-0.472***
[0.090]
-0.185**
[0.078]
Note: The table reports the full set of results of the switching regression model for Austria (cf. Table 4).
Standard errors clustered by person are in brackets and ***, ** and * denote 1, 5 and 10 percent
significance levels respectively. Table is continued on the next page.
31
Table A.3: Transaction-Level Cash Demand Austria: Switching Regression Model (Continued)
Wednesday
Thursday
Friday
Saturday
Typical week
Regime 1
-0.116**
[0.057]
-0.115**
[0.058]
-0.106*
[0.059]
-0.153***
[0.057]
0.037
[0.087]
Regime 0
0.046
[0.090]
0.076
[0.100]
-0.039
[0.104]
-0.002
[0.101]
0.070
[0.084]
3.954***
[0.162]
-0.081**
[0.037]
0.124**
[0.063]
1824.11
0.000
5.36
0.021
-9899.52
5790
739
3.981***
[0.192]
-0.156***
[0.047]
-0.065
[0.086]
Gas stations
(Semi)durables
Services
Restaurant/bar
Other exp.
Friends use less cash
Acceptance neighbours
Share shops 1 terminal
Share shops >1 terminals
Constant
Log σ
ρ
H0 : No Selection
(p-value)
H0 : β̃0 = β̃1
(p-value)
Log-Likelihood
Observations
Persons
Selection
-0.144*
[0.075]
-0.118
[0.077]
-0.128*
[0.077]
-0.103
[0.080]
0.209***
[0.070]
0.646***
[0.165]
0.125
[0.088]
-1.009***
[0.102]
-1.515***
[0.079]
-0.862***
[0.088]
-0.129*
[0.070]
1.193***
[0.311]
-1.254***
[0.320]
3.160***
[0.940]
0.014
[0.347]
Note: The table reports the full set of results of the switching regression model for Austria (cf. Table 4).
Standard errors clustered by person are in brackets and ***, ** and * denote 1, 5 and 10 percent
significance levels respectively.
32
Table A.4: Transaction-Level Cash Demand Canada: Switching Regression Model
Regime 1 Regime 0 Acceptance
Log transaction amount
0.094*** 0.186***
0.483***
[0.015]
[0.041]
[0.044]
2
Log transaction amount
-0.029***
[0.008]
Revolving credit
-0.180*** -0.122***
-0.008
[0.027]
[0.045]
[0.030]
Age 36-60
0.090*** 0.175*** -0.136***
[0.032]
[0.054]
[0.036]
Age 60+
0.246*** 0.392*** -0.216***
[0.047]
[0.082]
[0.053]
Educ. med
-0.095**
-0.071
0.130***
[0.037]
[0.057]
[0.038]
Educ. high
-0.078*
-0.056
0.196***
[0.040]
[0.064]
[0.042]
Female
0.231*** 0.160***
0.058*
[0.027]
[0.043]
[0.030]
Part-time
0.027
0.039
0.026
[0.044]
[0.067]
[0.047]
Unemployed
-0.142*** 0.201**
-0.155***
[0.052]
[0.081]
[0.058]
Retired
0.142*** 0.192***
-0.003
[0.039]
[0.067]
[0.044]
Income Q2
-0.001
0.027
0.089**
[0.032]
[0.052]
[0.035]
Income Q3
0.178*** 0.198***
0.136***
[0.038]
[0.063]
[0.046]
HH size 2-4
-0.04
-0.124**
0.057
[0.034]
[0.052]
[0.038]
HH size 4+
0.064
-0.433***
0.029
[0.061]
[0.092]
[0.069]
Note: The table reports the full set of results of the switching regression model for Canada (cf. Table 4).
Standard errors clustered by person are in brackets and ***, ** and * denote 1, 5 and 10 percent
significance levels respectively. The table is continued on the next page.
33
Table A.4: Transaction-Level Cash Demand Canada: Switching Regression Model (Continued)
Regime 1 Regime 0 Acceptance
3 to 6 registers
0.170***
[0.034]
More than 6 registers
0.350***
[0.045]
Gasoline
0.146**
[0.065]
Personal attire
0.079*
[0.047]
Healthcare
-0.204**
[0.088]
Hobby/Sporting
-0.216***
[0.040]
Services
-0.180***
[0.046]
Weekend
0.039
[0.034]
PM
0.142***
[0.031]
Urban
0.076*
[0.039]
Constant
3.470*** 3.418*** -0.772***
[0.088]
[0.109]
[0.092]
Log σ
0.100*** 0.052***
[0.010]
[0.019]
ρ
0.193***
-0.123
[0.064]
[0.126]
Ho: No Selection
10.43
p-value
0.001
4.68
Ho: β̃0 = β̃1
(p-value)
0.031
Log-likelihood
-20067.95
Observations
10020
Respondents
2808
Note: The table reports the full set of results of the switching regression model for Canada (cf. Table 4).
Standard errors clustered by person are in brackets and ***, ** and * denote 1, 5 and 10 percent
significance levels respectively.
34
Table B.1: Individual-Level Descriptive Statistics Austria
Dependent variables
Cash on hand (before diary)
Log cash on hand (before diary)
Explantory variables
Acceptance
ATM density
Risk of theft
Female
Unempl.
Other empl.
Student
Income Q2
Income Q3
Age 36-60
Age 60+
Edu med
Edu high
HH size 2-4
HH size 4+
HH head
Cash income
Share gas stations
Share (semi)durables
Share services
Share restaurant/bar
Share other exp.
Share TV Q2
Share TV Q3
Share TV Q4
Share AM
Share late PM
Share sunday
Share monday
Share tuesday
Share wednesday
Share thursday
Share friday
Instruments
Friends use less cash
Acceptance neighbours
Share shops 1 terminal
Share shops >1 terminals
Obs.
785
785
Obs.
785
785
785
785
785
785
785
785
785
785
785
785
785
785
785
785
785
785
785
785
785
785
785
785
785
785
785
785
785
785
785
785
785
Obs.
785
785
785
785
35
Mean
126.60
4.45
Mean
0.85
0.46
0.58
0.58
0.04
0.28
0.03
0.30
0.30
0.51
0.21
0.16
0.33
0.61
0.04
0.67
0.12
0.10
0.18
0.06
0.14
0.10
0.16
0.27
0.50
0.36
0.12
0.08
0.15
0.14
0.13
0.14
0.17
Mean
0.27
0.85
0.28
0.07
S.D.
132.63
0.92
S.D.
0.19
0.77
0.36
0.49
0.21
0.45
0.18
0.46
0.46
0.50
0.41
0.37
0.47
0.49
0.19
0.47
0.32
0.13
0.20
0.12
0.15
0.14
0.16
0.20
0.31
0.29
0.18
0.11
0.15
0.14
0.14
0.15
0.16
S.D.
0.44
0.10
0.12
0.04
Min
5.10
1.63
Min
0
0
0.10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Min
0
0.28
0
0
Max
1500
7.31
Max
1
3.28
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0.78
0.89
0.80
1
1
1
1
1
1
1
0.76
0.81
1
0.85
0.90
0.95
Max
1
1
0.68
0.31
Table B.2: Individual-Level Descriptive Statistics Canada
Dependent
Cash on hand (before diary)
Log cash on hand (before diary)
Explantory
Acceptance
Revolving credit
Age 36-60
Age 60+
Educ. med
Educ. high
Female
Part-time
Unemployed
Retired
Income Q2
Income Q3
HH size 2-4
HH size 4+
Gasoline value share
Personal attire value share
Healthcare value share
Hobby/Sporting value share
Services value share
TVQ2 value share
TVQ3 value share
TVQ4 value share
AM value share
Weekend value share
Instruments
share reg2
share reg3
share reg2sq
share reg3sq
share reg2cubic
share reg3cubic
Obs.
2808
2808
Obs.
2808
2808
2808
2808
2808
2808
2808
2808
2808
2808
2808
2808
2808
2808
2808
2808
2808
2808
2808
2808
2808
2808
2808
2808
Obs.
2808
2808
2808
2808
2808
2808
36
Mean
82.09
3.71
Mean
0.75
0.48
0.51
0.20
0.47
0.31
0.49
0.13
0.08
0.25
0.37
0.18
0.72
0.06
0.10
0.18
0.05
0.15
0.16
0.16
0.30
0.46
0.27
0.25
Mean
0.32
0.21
0.18
0.10
0.12
0.07
S.D.
207.34
1.25
S.D.
0.33
0.50
0.50
0.40
0.50
0.46
0.50
0.33
0.27
0.43
0.48
0.38
0.45
0.23
0.20
0.28
0.16
0.25
0.27
0.25
0.32
0.39
0.34
0.36
S.D.
0.27
0.24
0.24
0.20
0.23
0.18
Min
1
0
Min
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Min
0
0
0
0
0
0
Max
9065
9.11
Max
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Max
1
1
1
1
1
1
Table B.3: Transaction-Level Descriptive Statistics Austria
Dependent variables
Obs. Mean
S.D.
min
max
Cash on hand
5790 128.22 146.11 0.10 1500
Log cash on hand
5790 4.41
1
-2.30 7.31
Acceptance
5790 0.76
0.42
0
1
Explantory variables
Obs. Mean
S.D.
Min Max
Log transaction amount 5790
2.62
1.16
-1.77 6.11
Log transaction amount2 5790 8.23
6.18
0
37.30
Gas stations
5790 0.06
0.24
0
1
(Semi)durables
5790 0.13
0.34
0
1
Services
5790 0.05
0.22
0
1
Restaurant/bar
5790 0.18
0.38
0
1
Other exp.
5790 0.12
0.33
0
1
AM
5790 0.37
0.48
0
1
Late PM
5790 0.11
0.32
0
1
Sunday
5790 0.08
0.27
0
1
Tuesday
5790 0.15
0.36
0
1
Wednesday
5790 0.14
0.35
0
1
Thursday
5790 0.16
0.37
0
1
Friday
5790 0.15
0.36
0
1
Saturday
5790 0.16
0.37
0
1
Typical week
5790 0.75
0.43
0
1
Table B.4: Transaction-Level Descriptive Statistics Canada
Dependent variables
Obs. Mean S.D.
Min Max
Cash on hand
10020 97.14 166.66 0.02 9135
Log cash on hand
10020 3.99
1.13
-3.91 9.12
Acceptance
10020 0.74
0.44
0
1
Explanatory Variables
Obs. Mean S.D.
Min Max
Log transaction amount 10020 2.81
1.28
-1.56 8.27
Log transaction amount2 10020 9.51
7.55
0
68.37
Gasoline
10020 0.08
0.28
0
1
Personal attire
10020 0.16
0.37
0
1
Healthcare
10020 0.03
0.17
0
1
Hobby/Sporting
10020 0.22
0.41
0
1
Services
10020 0.14
0.34
0
1
Weekend
10020 0.26
0.44
0
1
PM
10020
0.7
0.46
0
1
Urban
10020 0.83
0.38
0
1
Revolving credit
10020
0.5
0.5
0
1
37